

The two algorithms need starting points
\(x^{(0)} \in \mathop {\bf int}(\mathop {\bf dom}\phi _\mathrm {p}) \cap \mathop {\bf dom}h\) ,
and \(z^{(0)} \in \mathop {\bf int}(\mathop {\bf dom}\phi _\mathrm {d})\) .
Conditions on stepsizes \(\sigma \) , \(\tau \)  will be specified later.
When Euclidean distances are used for the primal and dual proximal
operators, the two algorithms reduce to the primal and dual variants
of the Condat–Vũ algorithm (REF ) and (REF ),
respectively.
Algorithm () has been proposed in [1]}. Here
we discuss it together with () in a unified framework.
